Acronym	oho
TOCID symbol	O|C, aTT
Name	octahemioctahedron, facetorectified cube, allelotetratetrahedron
VRML	⭳ ©
Circumradius	1
Inradius wrt. {3}	+/− sqrt(2/3) = +/− 0.816497
Inradius wrt. {6}	0
Vertex figure	[3/2,6,3,6]/0
Snub derivation / VRML	⭳
Coordinates	(1/sqrt(2), 1/sqrt(2), 0)   & all permutations, all changes of sign
Volume	0
Surface	8 sqrt(3) = 13.856406
General of army	co
Colonel of regiment	co
Volume	0
Surface	8 sqrt(3) = 13.856406
Dihedral angles	between {3} and {6}:   arccos(1/3) = 70.528779°
Face vector	12, 24, 12
Confer	Grünbaumian relatives: oho+8{3}   compounds: iddei   general polytopal classes: Wythoffian polyhedra   analogs: retroexpanded simplex reSn   facetorectified hypercube frCn
External links

The octahemioctahedron is an edge-faceting of co, in fact it uses the triangles of it and all equatorial hexagons. In fact, the squares of its hull here become pseudo faces only.

When introducing a further vertex at the center and making face intersections into true edges, oho would become an edge-connected shape built from 8 tetrahedra.

This polyhedron could also be understood as a modwrap of that.

Incidence matrix according to Dynkin symbol

   x
3 / \ 3
 x---o
  3/2

x3/2o3x3*a

.   . .    | 12 |  2  2 | 1 2 1
-----------+----+-------+------
x   . .    |  2 | 12  * | 1 1 0
.   . x    |  2 |  * 12 | 1 0 1
-----------+----+-------+------
x3/2o .    |  3 |  3  0 | 4 * *
x   . x3*a |  6 |  3  3 | * 4 *
.   o3x    |  3 |  0  3 | * * 4

snubbed forms: β3/2o3x3*a, x3/2o3β3*a, β3/2o3β3*a

(isotoxal)

12 |  4 | 2 2
---+----+----
 2 | 24 | 1 1
---+----+----
 3 |  3 | 8 *
 6 |  6 | * 4

β3o3x

both( . . . ) | 12 |  2  2 | 1 1 2
--------------+----+-------+------
both( . . x ) |  2 | 12  * | 0 1 1
sefa( β3o . ) |  2 |  * 12 | 1 0 1
--------------+----+-------+------
      β3o .   ♦  3 |  0  3 | 4 * *
both( . o3x ) |  3 |  3  0 | * 4 *
sefa( β3o3x ) |  6 |  3  3 | * * 4

starting figure: x3o3x

β3/2x3x

demi( .   . . ) | 12 |  2  2 | 2 1 1
----------------+----+-------+------
both( .   x . ) |  2 | 12  * | 1 1 0
both( .   . x ) |  2 |  * 12 | 1 0 1
----------------+----+-------+------
both( .   x3x ) |  6 |  3  3 | 4 * *
      β3/2x .   ♦  3 |  3  0 | * 4 *
sefa( β3/2x3x ) |  3 |  0  3 | * * 4

starting figure: x3/2x3x